Imagine you’re a student beginning classes in woodwork. You show up at your first lesson full of excitement at the prospect of learning a new set of skills. The teacher announces, “Today we will be studying spanners.” There is a large selection of spanners of all sizes and shapes, there are nuts and bolts big and small. You spend the class using all the different spanners and getting good at picking the right spanner to match and bolt and you also get faster at using the tool.

The lesson ends, and you’re looking forward to the next one.

The next lesson comes around, this time the teacher announces, “Today we will be studying hammers.” There is a large selection of different types of hammers and you spend the lesson hammering different sized nails into different types of material.

The lessons continue in this way, the next lesson you learn saws, the next sandpaper, the next hot glue guns and so on.

By the end of the semester you think about your woodwork classes. You realise that you know how to use a lot of different tools, but you never actually got to make anything with those tools. You look back and wonder: what was the point of all that?

This is the current state of mathematics education. We make students go to class and learn about how to use all sorts of tools. One week they’ll study trigonometry, the next probability, the next algebra and so on. They do this week after week, year after year, getting better and better at using a variety of tools, but they never actually get to DO anything with those tools.